Conservation laws and symmetries of a generalized Kawahara equation

Abstract

The generalized Kawahara equation $u_t=a(t)u_{xxxxx}+b(t)u_{xxx}+c(t)f(u)u_x$ appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation $u_t=\alpha u{u}_x+\beta u^2{u}_x+\gamma u_{xxx}+\mu u_{xxxxx}$. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

6 pages